Question

SupposeX1andX2are independent with Γ(α,1) and Γ(α+12,1) distributions. LetY= 2√X1X2.FindEYandvar(Y).

Answer 1

E(Y) = √a + √(a+12)

Explanation:

X1 and X2 are independent variables while Y is the dependent variable, such that

Y = f(X1, X2)

Meaning Y is a function of X1 and X2

In this case,

Y = 2√X1X2

When (X1, X2) = (a, 1) ; Y = 2√a

When (X1, X2) = (a+12, 1) ; Y = 2√a+12

The expected value of Y is

[2√a + 2√a+12] ÷ 2 = √a + √a+12